Students

STAT6183 – Introduction to Probability

2026 – Session 1, In person-scheduled-weekday, North Ryde

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff Unit Convenor
Jun Han
Contact via email
See iLearn for consultation hours.
Credit points Credit points
10
Prerequisites Prerequisites
Corequisites Corequisites
STAT6170
Co-badged status Co-badged status
STAT2173
Unit description Unit description

This unit consolidates and expands upon the material on probability introduced in STAT6170. The emphasis is on the understanding of probability concepts and their applications. Examples are taken from areas as diverse as biology, medicine, finance, sports, and the social and physical sciences. Topics include: the foundations of probability; probability models and their properties; some commonly used statistical distributions; relationships and association between variables; distribution of functions of random variables and sample statistics; approximations including the central limit theorem; and an introduction to the behaviour of random processes. Students will also gain experience in using simulations to demonstrate many of these concepts.

Important Academic Dates

Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates

Learning Outcomes

On successful completion of this unit, you will be able to:

  • ULO1: Analyse probability and conditional probability of an event by applying a probabilistic model for an experiment.
  • ULO2: Apply a range of strategies to find and interpret the moments of discrete and continuous  random variables including  their expected values and variances. 
  • ULO3: Apply the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) to find asymptotic distribution of a sample mean
  • ULO4: Analyse a bivariate probability distribution to find and interpret  corresponding covariances, correlations, marginal and conditional probability distributions.
  • ULO5: Apply Markov Chain (MC) theory to practical problems and tasks.
  • ULO6: Use statistical software and simulations to demonstrate various theoretical concepts.

General Assessment Information

Attendance and participation

We strongly encourage all students to participate actively in all learning activities. Regular engagement is crucial for your success in this unit, as these activities provide opportunities to deepen your understanding of the material, collaborate with peers, and receive valuable feedback from instructors, to assist in completing the unit assessments. Your active participation not only enhances your own learning experience but also contributes to a vibrant and dynamic learning environment for everyone.

Requirements to Pass this Unit

To pass this unit, you must:

  • Achieve a total mark equal to or greater than 50%.

Hurdle Assessments

There is no Hurdle Assessment in this unit.

Late Submission Policy

  • 5% penalty per day: If you submit your assessment late, 5% of the total possible marks will be deducted for each day (including weekends), up to 7 days.

    • Example 1 (out of 100): If you score 85/100 but submit 20 hours late, you will lose 5 marks and receive 80/100.

    • Example 2 (out of 30): If you score 27/30 but submit 1 day late, you will lose 1.5 marks and receive 25.5/30.

  • After 7 days: Submissions more than 7 days late will receive a mark of 0.

  • Extensions:

    • Automatic short extension: Some assessments are eligible for automatic short extension. You can only apply for an automatic short extension before the due date.

    • Special Consideration: If you need more time due to serious issues and for any assessments that are not eligible for Short Extension, you must apply for Special Consideration.

Need help? Review the Special Consideration page HERE.

Assessments where Late Submissions will be accepted:

  • Assignments – YES, Standard Late Penalty applies;
  • Skill Exercise – YES, Standard Late Penalty applies;
  • Final Exam – NO, unless Special Consideration is granted.

Special Consideration

The Special Consideration Policy aims to support students who have been impacted by short-term circumstances or events that are serious, unavoidable, and significantly disruptive, and which may affect their performance in assessment. If you experience circumstances or events that affect your ability to complete the assessments in this unit on time, please inform the convenor and submit a Special Consideration request through https://connect.mq.edu.au.

Written Assessments/Quizzes/Tests: If you experience circumstances or events that affect your ability to complete the written assessments in this unit on time, please inform the convenor and submit a Special Consideration request through https://connect.mq.edu.au.

Assessment Tasks

Name Weighting Hurdle Due Groupwork/Individual Short Extension AI assisted?
Assignment 25% No 20/03/2026 Individual No Open AI
Skill exercise 25% No 29/05/2026 Individual No Open AI
Final Examination 50% No Exam Period Individual No Observed

Assignment

Assessment Type 1: Problem-based task
Indicative Time on Task 2: 10 hours
Due: 20/03/2026
Weighting: 25%
Groupwork/Individual: Individual
Short extension 3: No
AI assisted?: Open

You will reinforce your understanding by applying the concepts and skills from this unit to solve a set of problems.


On successful completion you will be able to:
  • Analyse probability and conditional probability of an event by applying a probabilistic model for an experiment.
  • Apply a range of strategies to find and interpret the moments of discrete and continuous  random variables including  their expected values and variances. 
  • Apply the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) to find asymptotic distribution of a sample mean
  • Analyse a bivariate probability distribution to find and interpret  corresponding covariances, correlations, marginal and conditional probability distributions.

Skill exercise

Assessment Type 1: Experiential task
Indicative Time on Task 2: 14 hours
Due: 29/05/2026
Weighting: 25%
Groupwork/Individual: Individual
Short extension 3: No
AI assisted?: Open

You will reinforce your understanding by applying the concepts and skills from this unit to solve a set of problems, presented in both paper-based and pre-recorded video formats.


On successful completion you will be able to:
  • Analyse probability and conditional probability of an event by applying a probabilistic model for an experiment.
  • Apply a range of strategies to find and interpret the moments of discrete and continuous  random variables including  their expected values and variances. 
  • Apply the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) to find asymptotic distribution of a sample mean
  • Analyse a bivariate probability distribution to find and interpret  corresponding covariances, correlations, marginal and conditional probability distributions.
  • Apply Markov Chain (MC) theory to practical problems and tasks.
  • Use statistical software and simulations to demonstrate various theoretical concepts.

Final Examination

Assessment Type 1: Examination
Indicative Time on Task 2: 10 hours
Due: Exam Period
Weighting: 50%
Groupwork/Individual: Individual
Short extension 3: No
AI assisted?: Observed

You will complete a formal invigilated examination to demonstrate your achievement of the unit’s learning outcomes by recalling, applying, and evaluating key concepts.


On successful completion you will be able to:
  • Analyse probability and conditional probability of an event by applying a probabilistic model for an experiment.
  • Apply a range of strategies to find and interpret the moments of discrete and continuous  random variables including  their expected values and variances. 
  • Apply the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) to find asymptotic distribution of a sample mean
  • Analyse a bivariate probability distribution to find and interpret  corresponding covariances, correlations, marginal and conditional probability distributions.
  • Apply Markov Chain (MC) theory to practical problems and tasks.

1 If you need help with your assignment, please contact:

  • the academic teaching staff in your unit for guidance in understanding or completing this type of assessment
  • the Writing Centre for academic skills support.

2 Indicative time-on-task is an estimate of the time required for completion of the assessment task and is subject to individual variation.

3 An automatic short extension is available for some assessments. Apply through the Service Connect Portal.

Delivery and Resources

Classes

Workshops (beginning in Week 1): There is one 1-hour workshop each week. During this hour, we will provide a brief overview of the week's content, run a Q&A session, and engage in some interesting activities together. 

Pre-recorded Lectures (released weekly from Week 1): There are no formal live lectures scheduled for this unit. Each week, we will have some video recordings covering the unit materials.

SGTA classes (beginning in Week 2): Students must register for and attend one 2-hour class per week.

The timetable for classes can be found on the University website at: https://publish.mq.edu.au

Enrolment can be managed using eStudent at: https://students.mq.edu.au/support/technology/systems/estudent

Technology Used and Required

This subject requires the use of the following computer software:

  • R: R software (freely available online) will be used in the unit. Students need to practice how to use the software and are expected to use R for the assignment. Students should also note that the final examination may contain inline R codes and output that students need to interpret to answer the questions.

Students are invited to bring their own devices (BYOD), and a laptop is recommended. Acceptable platforms are Windows, Linux, and Mac. 

Suggested textbooks

There is no required textbook for this unit. Students may benefit from having access to the following background reference for additional reading and problems:

  • Wackerly, D. D., Mendenhall, W., Scheaffer, R. L. Mathematical Statistics with Applications (4th,5th, 6th or 7th Editions)

The following books may also be useful background references:

  • Ross, S. A First Course in Probability, Pearson (5th, 6th, 7th, 8th or 9th Editions)
  • Ward, M. D. and Gundlach, E. (2016) Introduction to Probability, W. H. Freeman and Company
  • Kinney, J.J. (1997) Probability - An Introduction with Statistical Applications, John Wiley and Sons
  • Scheaffer R.L. (1994) Introduction to Probability and Its Applications, (2nd Edition) Duxbury Press
  • Sincich,T., Levine, D.M., Stephan, D. (1999) Practical Statistics by Example using Microsoft Excel

At least one copy of each of these is available in the Library, and extra copies may be available on the shelves for borrowing purposes.

Communication

We will communicate with you via your university email or through announcements on iLearn. Queries to convenors can either be placed on the iLearn discussion forum or sent to your lecturers from your university email address.

Unit Schedule

Week Material Covered
1 Experiments, sample spaces, Probability Rules, Permutations and Combinations.
2 Conditional Probability. Independence, Bayes’ Theorem.
3 Random Variables. Probability Functions, Discrete Probability Distributions, Cumulative Distribution functions,  Expected value and Variance. Moments.
4 Important Discrete Distributions: Bernoulli, Binomial, Geometric and Poisson.
5 Moment generating functions. Discrete Distributions: Negative Binomial and Hypergeometric.
6 Introduction to Continuous random variables. Cumulative distribution function.
  Session 1 Break
7 Continuous Distributions: Uniform, Exponential.
8 Normal Distribution.
9 Continuous Distributions: Gamma and Beta Distributions. Chebyshev’s Theorem.
10 Sampling Distributions.
11 Joint Distributions: Discrete and Continuous cases. 
12 Introduction to stochastic processes. Markov Chains.
13 Revision.

Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central (https://policies.mq.edu.au). Students should be aware of the following policies in particular with regard to Learning and Teaching:

Students seeking more policy resources can visit Student Policies (https://students.mq.edu.au/support/study/policies). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.

To find other policies relating to Teaching and Learning, visit Policy Central (https://policies.mq.edu.au) and use the search tool.

Student Code of Conduct

Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/admin/other-resources/student-conduct

Results

Results published on platform other than eStudent, (eg. iLearn, Coursera etc.) or released directly by your Unit Convenor, are not confirmed as they are subject to final approval by the University. Once approved, final results will be sent to your student email address and will be made available in eStudent. For more information visit connect.mq.edu.au or if you are a Global MBA student contact globalmba.support@mq.edu.au

Academic Integrity

At Macquarie, we believe academic integrity – honesty, respect, trust, responsibility, fairness and courage – is at the core of learning, teaching and research. We recognise that meeting the expectations required to complete your assessments can be challenging. So, we offer you a range of resources and services to help you reach your potential, including free online writing and maths support, academic skills development and wellbeing consultations.

Student Support

Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/

Academic Success

Academic Success provides resources to develop your English language proficiency, academic writing, and communication skills.

The Library provides online and face to face support to help you find and use relevant information resources. 

Student Services and Support

Macquarie University offers a range of Student Support Services including:

Student Enquiries

Got a question? Ask us via the Service Connect Portal, or contact Service Connect.

IT Help

For help with University computer systems and technology, visit http://www.mq.edu.au/about_us/offices_and_units/information_technology/help/

When using the University's IT, you must adhere to the Acceptable Use of IT Resources Policy. The policy applies to all who connect to the MQ network including students.

Changes from Previous Offering

The previous 2-hour lecture has been replaced with pre-recorded lecture videos and a 1-hour workshop. The videos introduce the core statistical concepts, and you are expected to review them before class. The workshop will focus on worked examples, problem-solving, and questions to help you apply the material and prepare for the assessments.

To enable students more time to focus on learning, understanding, and reflecting on the content of our unit, we have revised the assessment structure as follows. There are now only three assessments: an assignment, a skill exercise, and a final exam. Although no marks are associated with attendance, all activities provide you with key content designed to help you understand the content and complete the assessments.


Unit information based on version 2026.02 of the Handbook